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On the structure of A-free measures and applications

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de Philippis, Guido and Rindler, Filip (2016) On the structure of A-free measures and applications. Annals of Mathematics, 184 (3). pp. 1017-1039. doi:10.4007/annals.2016.184.3.10 ISSN 0003-486X.

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Official URL: https://doi.org/10.4007/annals.2016.184.3.10

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Abstract

We establish a general structure theorem for the singular part of A-free Radon measures, where A is a linear PDE operator. By applying the theorem to suitably chosen differential operators A, we obtain a simple proof of Alberti’s rank-one theorem and, for the first time, its extensions to functions of bounded deformation (BD). We also prove a structure theorem for the singular part of a finite family of normal currents. The latter result implies that the Rademacher theorem on the differentiability of Lipschitz functions can hold only for absolutely continuous measures and that every top-dimensional Ambrosio–Kirchheim metric current in Rd is a Federer–Fleming flat chain.

Item Type: Journal Article
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science, Engineering and Medicine > Science > Mathematics
Library of Congress Subject Headings (LCSH): Radon measures, Differential equations, Partial
Journal or Publication Title: Annals of Mathematics
Publisher: Mathematical Sciences Publishers
ISSN: 0003-486X
Official Date: 16 September 2016
Dates:
DateEvent
16 September 2016Published
7 April 2016Accepted
25 January 2016Submitted
Volume: 184
Number: 3
Page Range: pp. 1017-1039
DOI: 10.4007/annals.2016.184.3.10
Status: Peer Reviewed
Publication Status: Published
Access rights to Published version: Restricted or Subscription Access
Date of first compliant deposit: 6 May 2016
Date of first compliant Open Access: 16 October 2018
Funder: Italy. Ministero dell'istruzione, dell'università e della ricerca (MIUR), Engineering and Physical Sciences Research Council (EPSRC)
Grant number: RBSI14RVEZ (MIUR), EP/L018934/1 (EPSRC)
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